In a study to determine the performance of processing machines used to add raisins to trial-size "Raisin Bran" cereal boxes, (see Example 12.3 in Chapter 12), 6 sample boxes are taken at random from each machine's production line and the number of raisins in each box counted. The result for machines 3 and 4 are shown below. Assume that these can be considered as random samples from a normal population.
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Machine 3
13
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Machine 4
7
|
|
7
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4
|
|
11
|
7
|
|
9
|
7
|
|
12
|
12
|
|
18
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18
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(i) If the target average number of raisins dispensed per box is 10, by carrying out appropriate hypothesis tests determine which of the two machines is operating according to target and which is not. State the p-value associated with each test.
(ii) Is there any signi?cant difference between the mean number of raisins dispensed by these two machines? Support your answer adequately.